共查询到19条相似文献,搜索用时 328 毫秒
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本文针对正交表和置换群中的置换矩阵问题,提出了r-置换矩阵的概念,研究了其性质,并且给出这类矩阵逆的求法以及利用Hadamard积得出确定方阵为r-置换矩阵的充要条件,对于我们研究和推广置换矩阵有极其重要的意义。 相似文献
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本文研究了任意有限布尔代数上的置换矩阵的特征,根据此特征可构造各种类型的置换矩阵,并给出了n阶置换矩阵个数的计数公式,然后证明了n阶矩阵A可逆的充分必要条件是A为n阶置换矩阵. 相似文献
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利用矩阵的Kronecker积定义了一种矩阵乘积"*积",并且对这种乘积的性质进行了研究,发现它对于任意两个矩阵都有意义而且具有通常矩阵乘积的所有性质,并且在一些特殊情况下它比通常的矩阵乘积更和谐对称,而且当在"合适维数"下它就是通常的矩阵乘积,所以可以把这种"*积"看作是对通常矩阵乘积的推广. 相似文献
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消错学的错误矩阵可表达错误逻辑里所定义的分解、相似、增加、置换、毁灭、单位变换等转化词,针对其中的置换变换,构建了二类1错误矩阵方程增优置换变换错误矩阵方程,并讨论了该类错误矩阵方程的求解.用交通管理问题对错误矩阵进行了举例,并构建相应的错误矩阵方程,利用上述的求解方法,对二类1方程置换变换进行了求解. 相似文献
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广义正定矩阵的Hadamard积和Kronecker积的一些性质 总被引:11,自引:0,他引:11
本文讨论了各类型广义正定矩阵的 Hadamard 积和 Kronecker 积的一些重要性质,得到了判断 n 阶实矩阵是广义正定矩阵的一些充要条件,它们是[1]-[4]中相应定理的推广,最后,我们修正了[4]中的一个错误。 相似文献
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雷中平 《数学的实践与认识》1983,(1)
<正> 设 A 是 m×n 矩阵,P 和 Q 分别是 m 阶和 n 阶的置换方阵,我们称 A 和 PAQ 置换相抵.当 m=n,Q=P~(-1)=P~T时(这里 M~T 表示矩阵 M 的转置矩阵),A 和 PAP~T 称为置换相似.实际上,PAQ 是分别对 A 的行作置换(通过左乘 P)和对列作置换(通过右乘Q)后所得;而 PAP~T 则是对 A 的行和列分别作同样的置换后所得.注意到在作这些置换时,A 的每个元素本身并没有改变,只是其所在的位置变动了.置换相抵和置换相似是非常特殊的矩阵相抵变换和相似变换.特别地,在不少场合,A 有相当一部分元素是0,但它们散布各处.如能在对 A 进行其它运算或处理前,先通过置换相抵或置换相似变换把A 中的0元素尽可能有规律地集中成块,从而提供一个良好的初始状态,这对解决问题来说,常有事半功倍之效.所以,可以认为,置换相抵和置换相似又是一种最基本的相抵变 相似文献
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关于“|AB|=|A||B|”的一个证明方法 总被引:2,自引:0,他引:2
对于“矩阵积的行列式等于矩阵行列式之积”的证明.在现行的教课书上有两种.一般的采用Laplace定理给出行列式相乘规则结合矩阵相乘的定义来证明,面张禾端、郝鈵新的《高等代数》由于其编写体系的特点,则借用初 相似文献
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Let be the group of monomial matrices, i.e., the group generated by all permutation matrices and diagonal matrices in . The group acts on the set of all subspaces of . The number of orbits of this action, denoted by Nn,q, is the number of non-equivalent linear codes in . It was conjectured by Lax that as n→∞. We confirm this conjecture in this paper. 相似文献
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We consider the logarithm of the characteristic polynomial of random permutation matrices, evaluated on a finite set of different points. The permutations are chosen with respect to the Ewens distribution on the symmetric group. We show that the behavior at different points is independent in the limit and are asymptotically normal. Our methods enable us to study also the wreath product of permutation matrices and diagonal matrices with i.i.d. entries and more general class functions on the symmetric group with a multiplicative structure. 相似文献
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Journal of Theoretical Probability - We study the limiting behavior of smooth linear statistics of the spectrum of random permutation matrices in the mesoscopic regime, when the permutation follows... 相似文献
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Explicit forms are given for all commutative sets of permutation matrices which sum to a positive matrix, and for nonabelian groups of permutation matrices of order twice an odd prime which sum to the matrix of all ones. A relationship to circulants of level k is indicated. 相似文献
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Jessica Striker 《Discrete Mathematics》2011,(21):331
We present a direct bijection between descending plane partitions with no special parts and permutation matrices. This bijection has the desirable property that the number of parts of the descending plane partition corresponds to the inversion number of the permutation. Additionally, the number of maximum parts in the descending plane partition corresponds to the position of the one in the last column of the permutation matrix. We also discuss the possible extension of this approach to finding a bijection between descending plane partitions and alternating sign matrices. 相似文献
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A generic matrix \(A\in \,\mathbb {C}^{n \times n}\) is shown to be the product of circulant and diagonal matrices with the number of factors being \(2n-1\) at most. The demonstration is constructive, relying on first factoring matrix subspaces equivalent to polynomials in a permutation matrix over diagonal matrices into linear factors. For the linear factors, the sum of two scaled permutations is factored into the product of a circulant matrix and two diagonal matrices. Extending the monomial group, both low degree and sparse polynomials in a permutation matrix over diagonal matrices, together with their permutation equivalences, constitute a fundamental sparse matrix structure. Matrix analysis gets largely done polynomially, in terms of permutations only. 相似文献
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M. Abreu D. Labbate R. Salvi N. Zagaglia Salvi 《Linear algebra and its applications》2008,429(1):367-375
In this paper we investigate generalized circulant permutation matrices of composite order. We give a complete characterization of the order and the structure of symmetric generalized k-circulant permutation matrices in terms of circulant and retrocirculant block (0, 1)-matrices in which each block contains exactly one or two entries 1. In particular, we prove that a generalized k-circulant matrix A of composite order n = km is symmetric if and only if either k = m − 1 or k ≡ 0 or k ≡ 1 mod m, and we obtain three basic symmetric generalized k-circulant permutation matrices, from which all others are obtained via permutations of the blocks or by direct sums. Furthermore, we extend the characterization of these matrices to centrosymmetric matrices. 相似文献
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ABSTRACTIn this paper, we study a particular class of matrices generated by generalized permutation matrices corresponding to a subgroup of some permutation group. As applications, we first present a technique from which we can get closed formulas for the roots of many families of polynomial equations with degree between 5 and 10, inclusive. Then, we describe a tool that shows how to find solutions to Fermat's last theorem and Beal's conjecture over the square integer matrices of any dimension. Finally, simple generalizations of some of the concepts in number theory to integer square matrices are presented. 相似文献